scholarly journals Approximation of a simply supported plate with obstacle

2017 ◽  
Vol 23 (3) ◽  
pp. 348-358
Author(s):  
Cornel M Murea ◽  
Dan Tiba
Keyword(s):  
Variational Inequalities ◽  
Linear Equations ◽  
Numerical Examples ◽  
Simply Supported ◽  
Fixed Domain ◽  
Rigid Obstacle ◽  
Coincidence Set

We discuss an algorithm for the solution of variational inequalities associated with simply supported plates in contact with a rigid obstacle. Our approach has a fixed domain character, uses just linear equations and approximates both the solution and the corresponding coincidence set. Numerical examples are also provided.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

Vibration Control for the Rotor-Bearing System and Calculation of the Optimum Control Forces

1989 ◽  
Vol 111 (4) ◽  
pp. 366-369
Author(s):  
Lie Yu ◽  
You-Bai Xie ◽  
Jun Zhu ◽  
Damou Qiu
Keyword(s):  
Linear Equations ◽  
Mode Analysis ◽  
Constrained Control ◽  
Optimum Control ◽  
Numerical Examples ◽  
Rotor Bearing ◽  
Optimum Response ◽  
Control Forces ◽  
Complex Methods ◽  
Bearing System

The objective function applied to express the optimum response of the rotor-bearing system is presented based on the complex mode analysis. Two kinds of problems about the calculation of control forces are solved: in the nonconstraint condition the optimization of control forces is treated as the evaluation of a set of linear equations; and the Powell and complex methods are used to calculate the constrained control forces. Numerical examples are also given.

scholarly journals Second degree generalized Jacobi iteration method for solving system of linear equations

2016 ◽  
Vol 47 (2) ◽  
pp. 179-192
Author(s):  
Tesfaye Kebede Enyew
Keyword(s):  
Spectral Radius ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Jacobi Iteration ◽  
Optimal Values ◽  
Second Degree

In this paper, a Second degree generalized Jacobi Iteration method for solving system of linear equations, $Ax=b$ and discuss about the optimal values $a_{1}$ and $b_{1}$ in terms of spectral radius about for the convergence of SDGJ method of $x^{(n+1)}=b_{1}[D_{m}^{-1}(L_{m}+U_{m})x^{(n)}+k_{1m}]-a_{1}x^{(n-1)}.$ Few numerical examples are considered to show that the effective of the Second degree Generalized Jacobi Iteration method (SDGJ) in comparison with FDJ, FDGJ, SDJ.

The Analysis and Optimization of the Reliability of Laminates Based on Probabilistic and Non-Probabilistic Hybrid Model

2012 ◽  
Vol 629 ◽  
pp. 752-756 ◽  
Author(s):  
Wen Jie Peng ◽  
Xiao Xu Huang ◽  
Rui Ge
Keyword(s):  
Reliability Analysis ◽  
Hybrid Model ◽  
Reliability Index ◽  
Numerical Examples ◽  
Uncertainty Range ◽  
Probabilistic Uncertainty ◽  
Simply Supported ◽  
Uncertain Variables ◽  
Optimization Result

The reliability analysis and optimization of laminates containing probabilistic uncertain variables and non-probabilistic bounded uncertain variables is conducted in the present paper. Convex method is utilized to deal with non-probabilistic bounded uncertain variables. The reliability index and index range of a four sides simply supported laminate are optimized for numerical examples. The results indicate that considering the non-probabilistic uncertainty variables can get more conservative results, and the larger the uncertainty range of non-probabilistic bounded uncertain variables is, the more conservative optimization result is.

scholarly journals Second Derivative Free Eighteenth Order Convergent Method for Solving Non-Linear Equations

2017 ◽  
Vol 10 (04) ◽  
pp. 829-835
Author(s):  
V.B. Kumar Vatti ◽  
Ramadevi Sri ◽  
M.S.Kumar Mylapalli
Keyword(s):  
Linear Equations ◽  
Efficiency Index ◽  
Subject Classification ◽  
New Method ◽  
Second Derivative ◽  
Numerical Examples ◽  
Derivative Free ◽  
Convergent Method ◽  
And Performance ◽  
Non Linear Equations

In this paper, the Eighteenth Order Convergent Method (EOCM) developed by Vatti et.al is considered and this method is further studied without the presence of second derivative. It is shown that this method has same efficiency index as that of EOCM. Several numerical examples are given to illustrate the efficiency and performance of the new method. AMS Subject Classification: 41A25, 65K05, 65H05.

Certain efficient iterative methods for bipolar fuzzy system of linear equations

2020 ◽  
Vol 39 (3) ◽  
pp. 3971-3985 ◽  
Author(s):  
Muhammad Saqib ◽  
Muhammad Akram ◽  
Shahida Bashir
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Iterative Methods ◽  
Fuzzy Set ◽  
Fuzzy System ◽  
Linear Equations ◽  
Performance Validity ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Iterative Schemes

A bipolar fuzzy set model is an extension of fuzzy set model. We develop new iterative methods: generalized Jacobi, generalized Gauss-Seidel, refined Jacobi, refined Gauss-seidel, refined generalized Jacobi and refined generalized Gauss-seidel methods, for solving bipolar fuzzy system of linear equations(BFSLEs). We decompose n ×  n BFSLEs into 4n ×  4n symmetric crisp linear system. We present some results that give the convergence of proposed iterative methods. We solve some BFSLEs to check the validity, efficiency and stability of our proposed iterative schemes. Further, we compute Hausdorff distance between the exact solutions and approximate solution of our proposed schemes. The numerical examples show that some proposed methods converge for the BFSLEs, but Jacobi and Gauss-seidel iterative methods diverge for BFSLEs. Finally, comparison tables show the performance, validity and efficiency of our proposed iterative methods for BFSLEs.

On a non-stationary, non-Newtonian lubrication problem with Tresca fluid-solid law

2019 ◽  
Vol 27 (5) ◽  
pp. 719-730 ◽  
Author(s):  
Djamila Benterki ◽  
Hamid Benseridi ◽  
Mourad Dilmi
Keyword(s):  
Theoretical Analysis ◽  
Variational Inequalities ◽  
Variational Formulation ◽  
Reynolds Equation ◽  
Three Dimensional ◽  
Dynamic Regime ◽  
Thin Domain ◽  
Problem Statement ◽  
Friction Law ◽  
Fixed Domain

Abstract The paper deals with the theoretical analysis of a non-Newtonian lubrication problem in a dynamic regime in a three-dimensional thin domain {\Omega^{\varepsilon}} with Tresca friction law. The problem statement and variational formulation of the problem are formulated. Then the problem is reformulated in a fixed domain, in which case the estimates on velocity and pressure are proved. These estimates are useful in order to give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.

Automated Formation of Closed Form Kinematic Displacement Polynomials for Open Loop Planar and Spatial Chains

1995 ◽  
Vol 117 (1) ◽  
pp. 83-88
Author(s):  
S. C. Jen ◽  
D. Kohli
Keyword(s):  
Closed Form ◽  
Linear Equations ◽  
Numerical Approach ◽  
Inverse Kinematic ◽  
Open Loop ◽  
Hand Position ◽  
Numerical Examples ◽  
Polynomial Type ◽  
Joint Variable ◽  
Direct Kinematics

A new numerical approach for determining inverse kinematic polynomials of manipulators is presented in this paper. Let the inverse kinematic polynomial of a manipulator in one revolute joint variable θi be represented by gnTn + gn-1Tn-1 + gn-2Tn-2 + • + g1T + go = 0. T = tanθi/2 and go, g1...gn are polynomial type functions of hand position variables. The coefficients g are expressed in terms of undetermined coefficients and hand position variables. Then the undetermined coefficients are evaluated by using direct kinematics and the solutions of sets of linear equations, thus determining coefficients g and the inverse kinematic polynomial. The method is general and may be applied for determining inverse kinematic polynomials of any manipulator. However, the number of linear equations required in determining coefficients g become significantly larger as the number of links and the degrees of the manipulator increase. Numerical examples of 2R planar and 3R spatial manipulator are presented for illustration.

scholarly journals Hygrothermo-mechanical behaviour of layered composite plates

2002 ◽  
Vol 24 (3) ◽  
pp. 142-150
Author(s):  
Tran Ich Thinh
Keyword(s):  
Finite Element ◽  
Mechanical Behaviour ◽  
Composite Plates ◽  
Layered Composite ◽  
Rectangular Plates ◽  
Fe Method ◽  
Third Order ◽  
Numerical Examples ◽  
Simply Supported ◽  
Displacement Theory

In this paper, a hygrothermo-mechanical behaviour of simply supported, composite layered rectangular plates is presented. The analysis is based on use of the Finite Element (FE) method and the full third-order displacement theory. Numerical examples are presented for symmetrically in-axis (0° /90° /90° /0°) and off-axis ( 45° / - 45° / -45° / 45°) layered rectangular plates.

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